Explore the vast range of titles available.

Consider any single graded marketing organization where depletion of manpower occurssince decisions, exit of personnel etc.. There is an assumption that the depletion due to voluntary exit is correlated. By assuming that the inter-involuntary exit times, inter-breaking decision times forms different modified renewal processes, estimate dmean and estimated variance of time to recruitment are determined. The stochastic model assuming that intercontact times between successive contacts as correlated random variables are proposedShock models with intercontact time have been obtained by assuming the threshold distribution as exponential. In this paper, it is assumed that threshold follows exponentialgeometric distribution.

The standard Markowitz Mean-Variance optimization model is a single-period portfolio selection approach where the exit-time (or the time-horizon) is deterministic. ?In this paper we study the Mean-Variance portfolio selection problem ?with ?uncertain ?exit-time ?when ?each ?has ?individual uncertain ?xit-time?, ?which generalizes the Markowitz's model?. ???We provide some conditions under which the optimal portfolio of the generalized problem is independent of the exit-times distributions. Also, ??it is shown that under some general circumstances, the sets of optimal portfolios? ?in the generalized model and the standard model are the same?.

We study the asymptotic behavior of a multidimensional random walk in a general cone. We find the tail asymptotics for the exit time and prove integral and local limit theorems for a random walk conditioned to stay in a cone. The main step in the proof consists in constructing a positive harmonic function for our random walk under minimal moment restrictions on the increments. For the proof of tail asymptotics and integral limit theorems, we use a strong approximation of random walks by Brownian motion. For the proof of local limit theorems, we suggest a rather simple approach, which combines integral theorems for random walks in cones with classical local theorems for unrestricted random walks. We also discuss some possible applications of our results to ordered random walks and lattice path enumeration.

Motivated by edge behaviour reported for biological organisms, we show that random walks with a bias at a boundary lead to a discontinuous probability density across the boundary. We continue by studying more general diffusion processes with such a discontinuity across an interior boundary. We show how hitting probabilities, occupancy times and conditional occupancy times may be solved from problems that are adjoint to the original diffusion problem. We highlight our results with a biologically motivated example, where we analyze the movement behaviour of an individual in a network of habitat patches surrounded by dispersal habitat.

Noise plays a fundamental role in a wide variety of physical and biological dynamical systems. It can arise from an external forcing or due to random dynamics internal to the system. It is well established that even weak noise can result in large behavioral changes such as transitions between or escapes from quasi-stable states. These transitions can correspond to critical events such as failures or extinctions that make them essential phenomena to understand and quantify, despite the fact that their occurrence is rare. This article will provide an overview of the theory underlying the dynamics of rare events for stochastic models along with some example applications.

We establish general moment estimates for the discrete and continuous exit times of a general It₁ process in terms of the distance to the boundary. These estimates serve as intermediate steps to obtain strong convergence results for the approximation of a continuous exit time by a discrete counterpart, computed on a grid. In particular, we prove that the discrete exit time of the Euler scheme of a diffusion converges in the L₁ norm with an order 1/2 with respect to the mesh size. This rate is optimal.

In this paper we develop a metastability theory for a class of stochastic reaction–diffusion equations exposed to small multiplicative noise. We consider the case where the unperturbed reaction–diffusion equation features multiple asymptotically stable equilibria. When the system is exposed to small stochastic perturbations, it is likely to stay near one equilibrium for a long period of time but will eventually transition to the neighborhood of another equilibrium. We are interested in studying the exit time from the full domain of attraction (in a function space) surrounding an equilibrium and, therefore, do not assume that the domain of attraction features uniform attraction to the equilibrium. This means that the boundary of the domain of attraction is allowed to contain saddles and limit cycles. Our method of proof is purely infinite dimensional, that is, we do not go through finite dimensional approximations. In addition, we address the multiplicative noise case, and we do not impose gradient type of assumptions on the nonlinearity. We prove large deviations logarithmic asymptotics for the exit time and for the exit shape, also characterizing the most probable set of shapes of solutions at the time of exit from the domain of attraction.

We prove a large deviation principle (LDP) for a general class of Banach space valued stochastic differential equations (SDEs) that is uniform with respect to initial conditions in bounded subsets of the Banach space. A key step in the proof is showing that a uniform LDP over compact sets is implied by a uniform over compact sets Laplace principle. Because bounded subsets of infinite-dimensional Banach spaces are in general not relatively compact in the norm topology, we embed the Banach space into its double dual and utilize the weak-⋆\\star compactness of closed bounded sets in the double dual space. We prove that a modified version of our SDE satisfies a uniform Laplace principle over weak-⋆\\star compact sets and consequently a uniform over bounded sets LDP. We then transfer this result back to the original equation using a contraction principle. The main motivation for this uniform LDP is to generalize results of Freidlin and Wentzell concerning the behavior of finite-dimensional SDEs. Here we apply the uniform LDP to study the asymptotics of exit times from bounded sets of Banach space valued small noise SDE, including reaction diffusion equations with multiplicative noise and two-dimensional stochastic Navier–Stokes equations with multiplicative noise.

A heat exchanger can be modeled as a closed domain containing an incompressible fluid. The moving fluid has a temperature distribution obeying the advection-diffusion equation, with zero temperature boundary conditions at the walls. Starting from a positive initial temperature distribution in the interior, the goal is to flux the heat through the walls as efficiently as possible. Here we consider a distinct but closely related problem, that of the integrated mean exit time of Brownian particles starting inside the domain. Since flows favorable to rapid heat exchange should lower exit times, we minimize a norm of the exit time. This is a time-independent optimization problem that we solve analytically in some limits and numerically otherwise. We find an (at least locally) optimal velocity field that cools the domain on a mechanical time scale, in the sense that the integrated mean exit time is independent on molecular diffusivity in the limit of large-energy flows.

Consider a Markov chain (Xn ) n ≥0 with values in the state space 𝕏. Let f be a real function on 𝕏 and set S n = Σ i = 1 n f X i , n ≥ 1 . Let ℙ x be the probability measure generated by the Markov chain starting at X 0 = x. For a starting point y ∈ ℝ, denote by τ y the first moment when the Markov walk (y + Sn ) n ≥1 becomes nonpositive. Under the condition that Sn has zero drift, we find the asymptotics of the probability ℙ x (τ y > n) and of the conditional law ℙ x ( y + S n ≤ · n | τ y > n ) as n → + ∞.