In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.). So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreo...

The multidimensional exponential Levy equations are used to describe many stochastic phenomena such as market fluctuations. Unfortunately in practice an exact solution does not exist for these equations. This motivates us to propose a numerical solution for n-dimensional exponential Levy equations by block pulse functions. We compute the jump integral of each block pulse function and present a ...

Abstract The Picard iteration method is used to study the existence and uniqueness of solutions for stochastic Volterra-Levin equation with variable delays. Several sufficient conditions are specified ensure that has a unique solution. First, transformed into an integral equation. Then, obtain solution equation, successive approximation sequences constructed, derived by convergence sequences. F...

‎in this paper‎, ‎we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain‎. ‎this problem consists of determining the temperature on the interior boundary curve from the cauchy data (boundary temperature and heat flux) on the exterior boundary curve‎. ‎to this end‎, ‎the boundary integral equation method is used‎. ‎since the resulting system of linea...

Let S t be the time t price of a particular stock. We know that if S t ∼ GBM (µ, σ 2), then S t = S 0 e (µ−σ 2 /2)t+σBt (1) where B t is the Brownian motion driving the stock price. An alternative possibility is to use a stochastic differential equation (SDE) to describe the evolution of S t. In this case we would write S t = S 0 + t 0 µS u du + t 0 σS u dB u (2) or in shorthand , dS t = µS t d...

We consider applications of path-integral methods to the analysis of a stochastic hybrid model representing a network of synaptically coupled spiking neuronal populations. The state of each local population is described in terms of two stochastic variables, a continuous synaptic variable and a discrete activity variable. The synaptic variables evolve according to piecewise-deterministic dynamic...

This article proposes a fast and accurate expansion-iterative method for solving second kind linear Volterra integral equations. The method is based on a special representation of vector forms of triangular functions (TFs) and their operational matrix of integration. By using this approach, solving the integral equation reduces to solve a recurrence relation. The approximate solution of integra...

The stochastic transport equation is considered where the randomness given by a symmetric integral with respect to measure. For measure, only σ-additivity in probability and continuity of paths assumed. Existence uniqueness weak solution are proved.

k=1 Gk(ω) · 1(uk,vk](s), ω ∈ Ω, s ≥ 0, where n ∈ N, 0 ≤ uk < vk, and Gk ∈ L(Fuk). We let Le denote the class of all such integrands. Notice that each H ∈ Le satisfies (i) s → Hs(ω) is a left-continuous step function for each ω ∈ Ω, (ii) Hs ∈ L(Fs) for each s ≥ 0, (iii) viewed as a mapping from Ω × [0, t] to R, (ω, s) → Hs(ω) is Ft ⊗B[0,t] measurable for each t > 0, and (iv) E[ ∫ t 0 H s ds] < ∞...