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Heavy tailed solutions of multivariate smoothing transforms
Heavy tailed solutions multivariate smoothing transforms Probability
2012/6/29
Let $N > 1$ be a fixed integer and $(C_1,..., C_N,Q)$ a random element of $GL(d, \R)^N x \R^d$. We consider solutions of multivariate smoothing transforms, i.e. random variables $R$ satisfying $$R \eq...
On the (strict) positivity of solutions of the stochastic heat equation
the stochastic heat equation Probability
2012/6/30
We give a new proof of the fact that the solutions of the stochastic heat equation, started with non-negative initial conditions, are strictly positive at positive times. The proof uses concentration ...
Local Holder continuity property of the Densities of Solutions of SDEs with Singular Coefficients
Malliavin Calculus non-smooth drift density function Probability
2012/6/21
We prove that the weak solution of a uniformly elliptic stochastic differential equation with locally smooth diffusion coefficient and H\"{o}lder continuous drift has a H\"{o}lder continuous density f...
Strictly stationary solutions of ARMA equations in Banach spaces
Strictly stationary solutions ARMA equations Banach spaces Probability
2012/6/21
We obtain necessary and sufficient conditions for the existence of strictly stationary solutions of ARMA equations in Banach spaces with independent and identically distributed noise under certain ass...
On the Comparison and Uniqueness for Solutions of BSDEs with Continuous Coefficients
Backward stochastic differential equation comparison theorem uniqueness
2011/11/5
As we known that there may be more than one solution for backward stochastic differential equation with continuous coefficients and the comparison theorem for any solutions of two BSDEs does not hold ...
Necessary and Sufficient Conditions for Positive and Negative Solutions of BSDEs with Continuous Coefficients
Backward stochastic differential equation positive solution continuous coefficients
2011/11/5
As we know that, in stochastic finance, each pricing mechanism corresponds to a well-defined BSDE. The behaviors of g exert an influence to this mechanism. In some circumstances, to regulate or to des...