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We study one-dimensional stochastic differential equations with nonhomogeneous coefficients and non-Lipschitz diffusion. We prove some properties of the solutions of such equations and of the corresponding Euler scheme. We obtain the convergence rate of the Euler scheme for diffusions with weak...
We consider a stock price Z t whose dynamics follows a geometric Brownian motion living on the standard Gaussian white noise space. We regard the risk-free interest rate r and volatility σσ as independent variables of the stock price. We show that the partial derivatives of the stock price with...
This paper stems from previous work of certain of the authors, where the issue of inducing distributions on lower dimensional spaces arose as a natural outgrowth of the main goal: the estimation of conditional probabilities, given other partially specified conditional probabilities as a premise...
In this paper we consider a backward stochastic differential equation driven by an infinite dimensional martingale. Our aim is to derive the existence and uniqueness of the solution to such an equation. The filtration we consider is an arbitrary right continuous one not necessarily the natural...
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