In this paper, multi-dimensional Wiener-Liu process is proposed. Wiener-Liu process is a type of hybrid process, it corresponds to Brownian motion (Wiener process) in stochastic process and Liu process in fuzzy process. In classical analysis, the basic operations are differential and integral. Correspondingly, Ito-Liu formula plays the role of Ito formula in stochastic process and Liu formula i...

the stochastic reaction diffusion systems may suffer sudden shocks‎, ‎in order to explain this phenomena‎, ‎we use markovian jumps to model stochastic reaction diffusion systems‎. ‎in this paper‎, ‎we are interested in almost sure exponential stability of stochastic reaction diffusion systems with markovian jumps‎. ‎under some reasonable conditions‎, ‎we show that the trivial solution of stocha...

in this paper, we present an application of the stochastic calculusto the problem of modeling electrical networks. the filtering problem have animportant role in the theory of stochastic differential equations(sdes). in thisarticle, we present an application of the continuous kalman-bucy filter for a rlcircuit. the deterministic model of the circuit is replaced by a stochastic model byadding a ...

In this paper, we present an application of the stochastic calculusto the problem of modeling electrical networks. The filtering problem have animportant role in the theory of stochastic differential equations(SDEs). In thisarticle, we present an application of the continuous Kalman-Bucy filter for a RLcircuit. The deterministic model of the circuit is replaced by a stochastic model byadding a ...

‎This paper develops iterative method described by [V‎. ‎Daftardar-Gejji‎, ‎H‎. ‎Jafari‎, ‎An iterative method for solving nonlinear functional equations‎, ‎J‎. ‎Math‎. ‎Anal‎. ‎Appl‎. ‎316 (2006) 753-763] to solve Ito stochastic differential equations‎. ‎The convergence of the method for Ito stochastic differential equations is assessed‎. ‎To verify efficiency of method‎, ‎some examples are ex...

Stochastic differential equations and the Black-Scholes PDE. We derived the BlackScholes formula by using arbitrage (risk-neutral) valuation in a discrete-time, binomial tree setting, then passing to a continuum limit. This section explores an alternative, continuoustime approach via the Ito calculus and the Black-Scholes differential equation. This material is very standard; I like Wilmott-How...

2 Brownian Motion 6 2.1 Kolmogorov’s Continuity Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 Working With Ito Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3 Stopping Times and Local Martingales . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.4 Ito Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

In this paper we look at several (trigonometric) stochastic differential equations, find the general form for such nonlinear equation by using I'to formula. Then exact solution different trigonometric equations use of integrals. Ilustrate approach with various examples. (Precise Ito integral formula) and approximate (numerical approximation (the Euler-Maruyama technique Milstein method) were co...

In this paper, we study a reducible method which is called linearization(Linear-transform) for some non-linear stochastic differential equations (SDEs) to linear by using the Ito-integrated formula. And then finding their analytic solution, compare obtained solution nonlinear SDEs with approximate numerical (Euler -Maruyama and Milstein) Methods.