Volumen 05 (2001) No. 2
Volumen 05 (2001) No. 2 
Degree and fixed point index. An account
Carlos Prieto
Resumen:
In this account, a development of the concepts of Brouwer degree and Lefschetz-Hopf fixed point index is discussed in the light of work done mainly by A. Dold, H. Ulrich and the author. Generalizations to certain coincidence situations including the equivariant cases are presented, as well as how to deal with the infinite dimensional cases. In two appendices a proof of the Lefschetz-Hopf theorem for these indices is referred to, as well as a generalization of Dold's fixed point transfer is sketched.
Existence of Nash equilibria in nonzero-sum ergodic stochastic games in Borel spaces
Rafael Benítez-Medina
Resumen:
In this paper we study nonzero-sum stochastic games with Borel state and action spaces, and the average payoff criterion. Under suitable assumptions we show the existence of Nash equlibria in stationary strategies. Our hypotheses include ergodicity conditions and an ARAT (additive reward, additive transition) structure.
Monte Carlo approach to insurance ruin problems using conjugate processes
Luis F. Hoyos-Reyes
Resumen:
In this paper is discussed a simulation method developed by S. Asmussen called conjugate processes which is based on a version of Wald's fundamental identity. With this method it is possible to simulate within finite time risk reserve processes with infinite time horizons. This allows us to construct Monte Carlo estimators for the ruin probability, which is one of the main problems in insurance risk theory. Some examples of the Poisson/Exponential and Poisson/Uniform cases are presented.
Sobre la estrechez de un espacio topológico
Alejandro Ramírez Páramo
Resumen:
En este trabajo se muestran algunos resultados sobre la estrechez en la clase ${\cal C}_{2}$ de los espacios Hausdorff y compactos; en particular, se demuestran las igualdades $t(X)=h\pi \chi (X)$ y $t(\prod \{X_{s}:s\in S\})=$ $| S | \cdot sup\{t(X_s):s \in S\}$, cuando $X$ y $X_{s}$ pertenecen a ${\cal C}_{2}$ para toda $s \in S$.
Medida de colisión de un $(\alpha, d, \beta)$-superproceso con su medida inicial
José Villa Morales
Resumen:
Sea $X=\{X_{t}:t\geq 0\}$ un $(\alpha ,d,\beta )$-Superproceso. Demostraremos que la medida de colisión, $M(X)$, de $X$ con su valor inicial $X_{0}$, definida heurísticamente por $M_{t}(X)(\varphi ):=\langle \varphi ((y+x)/2)\delta (y-x),X_{0}(dy)X_{t}(dx)\rangle $ existe. Más precisamente si $J_{\varepsilon }$, con $\varepsilon >0$, es un molificador, entonces $\lim_{\varepsilon \rightarrow 0}\langle \varphi ((y+x)/2)J_{\varepsilon }(y-x),X_{0}(dy)X_{t}(dx)\rangle $ existe en probabilidad para cada $\varphi \in C_{b}(R^{d})_{+}$.