79 research outputs found

    Kernel estimates for nonautonomous Kolmogorov equations

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    Using time dependent Lyapunov functions, we prove pointwise upper bounds for the heat kernels of some nonautonomous Kolmogorov operators with possibly unbounded drift and diffusion coefficients

    Analytic approach to solve a degenerate parabolic PDE for the Heston Model

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    We present an analytic approach to solve a degenerate parabolic problem associated to the Heston model, which is widely used in mathematical finance to derive the price of an European option on an risky asset with stochastic volatility. We give a variational formulation, involving weighted Sobolev spaces, of the second order degenerate elliptic operator of the parabolic PDE. We use this approach to prove, under appropriate assumptions on some involved unknown parameters, the existence and uniqueness of weak solutions to the parabolic problem on unbounded subdomains of the half-plane

    On vector-valued Schrödinger operators with unbounded diffusion in Lp spaces

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    We prove generation results of analytic strongly continuous semigroups on Lp(Rd, Rm) (1 < p< ∞) for a class of vector-valued Schrödinger operators with unbounded coefficients. We also prove Gaussian type estimates for such semigroups

    Instantaneous blowup and singular potentials on Heisenberg groups

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    In this paper we generalize the instantaneous blowup result from [3] and [15] to the heat equation perturbed by singular potentials on the Heisenberg group
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