@MISC{Samorodnitsky_tailbehavior, author = {Gennady Samorodnitsky}, title = {Tail Behavior of Shot Noise Processes}, year = {} }

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Abstract

We discuss the different ways heavy tails can arise in shot noise models and possible applications of the latter to financial modeling. 1 Introduction A shot noise process is a stochastic process of the form X(t) = X T i t R i (t \Gamma T i ); t 2 R; (1:1) where T i 's are the points of a point process, fN(A); A a Borel setg, and fR i (t); t 0g; i = 1; 2; : : : is a sequence of i.i.d. measurable stochastic processes, independent of the point process. Regarding X(t) as describing the state of a certain system at time t, there is a very natural interpretation of a model given by (1.1). Think of T i 's being the instances of time a "shock" arrives at the system. The effect of the shock at the system is a dynamic and random process. That is, h units of time later, at time T i + h this effect is equal to R i (h). The total state of the system at time t is then the sum of the effects of all shocks occurring up to that time. The stochastic processes fR i (t); t 0g; i = 1; 2; : : : are...